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In a market with one safe and one risky asset, an investor with a long horizon, constant investment opportunities, and constant relative risk aversion trades with small proportional transaction costs. We derive explicit formulas for the…
We adopt deep learning models to directly optimise the portfolio Sharpe ratio. The framework we present circumvents the requirements for forecasting expected returns and allows us to directly optimise portfolio weights by updating model…
We design an optimal strategy for investment in a portfolio of assets subject to a multiplicative Brownian motion. The strategy provides the maximal typical long-term growth rate of investor's capital. We determine the optimal fraction of…
Traders are often faced with large block orders in markets with limited liquidity and varying volatility. Executing the entire order at once usually incurs a large trading cost because of this limited liquidity. In order to minimize this…
The aim of this work consists in the study of the optimal investment strategy for a behavioural investor, whose preference towards risk is described by both a probability distortion and an S-shaped utility function. Within a continuous-time…
We introduce new mathematical methods to study the optimal portfolio size of investment portfolios over time, considering investors with varying skill levels. First, we explore the benefit of portfolio diversification on an annual basis for…
This paper investigates the optimal investment problem in a market with two types of illiquidity: transaction costs and search frictions. Extending the framework established by arXiv:2101.09936, we analyze a power-utility maximization…
We examine the problem of optimal portfolio allocation within the framework of utility theory. We apply exponential utility to derive the optimal diversification strategy and logarithmic utility to determine the optimal leverage. We enhance…
We develop a new analysis for portfolio optimisation with options, tackling the three fundamental issues with this problem: asymmetric options' distributions, high dimensionality and dependence structure. To do so, we propose a new…
Assume (1) asset returns follow a stochastic multi-factor process with time-varying conditional expectations; (2) investments are linear functions of factors. This paper calculates asymptotic joint moments of the logarithm of investor's…
We study a dynamic portfolio optimization problem related to convergence trading, which is an investment strategy that exploits temporary mispricing by simultaneously buying relatively underpriced assets and selling short relatively…
In this paper we derive the exact solution of the multi-period portfolio choice problem for an exponential utility function under return predictability. It is assumed that the asset returns depend on predictable variables and that the joint…
This paper explores the effectiveness of high-frequency options trading strategies enhanced by advanced portfolio optimization techniques, investigating their ability to consistently generate positive returns compared to traditional long or…
We consider an investor, whose portfolio consists of a single risky asset and a risk free asset, who wants to maximize his expected utility of the portfolio subject to the Value at Risk assuming a heavy tail distribution of the stock prices…
In this paper, as a first step in examining the properties of a feasible portfolio subset that is characterized by budget and risk constraints, we assess the maximum and minimum of the investment concentration using replica analysis. To do…
We study the problem of optimal trading using general alpha predictors with linear costs and temporary impact. We do this within the framework of stochastic optimization with finite horizon using both limit and market orders. Consistently…
We consider a two-way trading problem, where investors buy and sell a stock whose price moves within a certain range. Naturally they want to maximize their profit. Investors can perform up to $k$ trades, where each trade must involve the…
Despite the availability of very detailed data on financial market, agent-based modeling is hindered by the lack of information about real trader behavior. This makes it impossible to validate agent-based models, which are thus…
Computing risk measures of a financial portfolio comprising thousands of derivatives is a challenging problem because (a) it involves a nested expectation requiring multiple evaluations of the loss of the financial portfolio for different…
This paper studies the portfolio optimization problem when the investor's utility is general and the return and volatility of the risky asset are fast mean-reverting, which are important to capture the fast-time scale in the modeling of…